Valental aspects of Peircean algebraic logic

Abstract

This paper describes a system of logic that has both an algebraic syntax and a graphical syntax and that may be regarded as a kind of semantic net. The paper analyses certain "valental" characteristics of terms and graphs of this logical system: characteristics defined in terms of the "valence", or number of argument-places, in the terms and graphs. The most famous valental result is the so-called "Reduction Thesis" of Charles Sanders Peirce. The paper briefly explicates the author's proof, which is to be published in a forthcoming book, of this Reduction Thesis. Several additional valental results are proved, and the potential of PAL as a bridge between logic and topological graph theory is suggested. © 1992.